Question

A class of 30 students is conducting an experiment using a six-sided number cube. Each person rolls the number cube 6 times and charts their results. If the results are combined into a class list, which statement is false?
A.
Each individual student's data will match the theoretical data.
B.
The experimental probability of the combined data should be closer to the theoretical probability than most individual data probability.
C.
There is more of a chance a student won't get all 6 numbers in their rolls than will.
D.
Every student has the same probability of getting each individual number.

Answer 1

A is false.

Reasoning:
- A claims every student's 6 rolls will match the theoretical distribution (i.e., one of each face). The probability of getting all six different faces in 6 rolls is 6!/6^6 = 720/46656 ≈ 0.0154 (about 1.54%), so it is very unlikely each student's data will match theory.
- B is true by the law of large numbers: 180 combined rolls should be closer to 1/6 for each face than most individual 6-roll samples.
- C is true because the probability of getting all six faces in 6 rolls is only ~1.54%, so not getting all six is far more likely.
- D is true: each student’s single roll has the same probability 1/6 for each face.